The 25 year-old looked set for a move to Queens Park Rangers after they had themselves settled on a £5.5m fee with the Scottish Premier League champions on Wednesday.
However, the Canaries, who have been chasing the former Scunthorpe United man for some time appear to have stolen a march on their rivals after agreeing personal terms on a four year contract.
Hooper moved to Celtic Park back in 2010, and has scored sixty-three goals in ninety-five league appearances.
He also scored four goals in last season’s Champions League campaign; including two in the qualifying rounds, as well as hitting a brace in the Scottish Cup final victory over Hibernian back in May.
Norwich have already secured deals for fellow centre-forward Ricky Van Wolfswinkel, midfielders Leroy Fer and Nathan Redmond, defenders Martin Olsson, Semi Ajayi and Javier Garrido and goalkeeper Carlo Nash.